Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Problem Solving - Page 894: 47b

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Using the law of cosines $$10^2=(2x)^2+(3x)^2-2\times2x\times3x\cos 60^\circ\\100=4x^2+9x^2-6x^2\\7x^2=100\\x^2=\frac{100}{7}\\x=\pm \sqrt \frac{100}{7}\\x=\sqrt \frac{100}{7}\approx3.78$$ After $3.78$ hours, they won't be able to communicate with each other.